Put on a long-sleeved jacket or shirt that's thick with fabric to protect your arms and shoulders as you work near the pointed leaves of the yucca. Put on leather gloves once the jacket or shirt is on to cover bare skin. Eye goggles will prevent accidental poking of the leaf tips as you bend, stoop and lunge around the plant as you work.
Insert your arm carrying a sturdy-bladed pruning saw into the cluster of yucca stems. Saw off the base of each yucca stem as close to the ground as possible. Push or kick the toppled yucca stem away from you to gain access to the fresh pruning wound on the stump.
Pour a concentrated glyphosate-based herbicide onto the fresh, wet wound of each yucca stem base. Do this within 10 minutes of making the pruning cut. Use a 1-inch-wide or larger paintbrush to evenly coat the wound with the glyphosate. The stem tissues will absorb the chemical and begin to transport it throughout the underground root system, killing more of the plant.
Clear away all the cut yucca debris from the site. Make sure all stumps of the cut yucca plants have been thoroughly coated with glyphosate before they naturally callus and air dry.
Trim away any small leafy sprouts or immature rosettes of young yucca plants in the general area where you pruned. Remove all traces of the plant where green leaves remain, as photosynthesizing tissues provide food to the root system to create new growth.
Cover the area with a heavy canvas or dark-colored, opaque nylon car cover. Spread the covering over all chemical-treated stumps of the yucca plant. Secure the covering down with rocks, bricks or cinder blocks so no light reaches the plant stumps or adjacent surface roots.
Remove the sun-blocking covering every six months to monitor the progress of the yucca stumps' degradation and death. If new sprouts occur -- and they should be white in color because of the lack of light -- trim them off with hand pruners and again paint glyphosate herbicide on the fresh cutting wounds for absorption.